Accelerating Kalman Filter predict/update steps with NanoGEMM for small state matrices (2.5x speedup)

[eminsk]

Hi @rlabbe and contributors,

Thank you for maintaining filterpy!

In real-time robotics and navigation loops running at 500–1000 Hz, state and covariance matrix multiplications (typically 4x4 to 16x16) suffer from NumPy/BLAS fixed dispatch latency (3–5 µs per @ call).

We created a minimalist C microkernel called NanoGEMM designed specifically for sub-microsecond execution on small matrices via direct AVX2+FMA and ARM NEON register tiling.

Micro-benchmark on 8x8 & 16x16 covariance update:

• NumPy @: ~3.2 µs per iteration
• NanoGEMM: ~1.1 µs per iteration (2.9x faster)

It can be integrated as an optional drop-in acceleration with a zero-friction fallback:

try:
    import nanogemm as ng
    _matmul = ng.matmul
except ImportError:
    _matmul = np.matmul

This would give robotics and sensor fusion pipelines a 2-3x speedup on CPU without adding any mandatory dependencies.

Would you be open to a lightweight PR introducing an optional fast path?

• Repo: https://github.com/eminsk/nanogemm
• Benchmark / Demo: https://colab.research.google.com/github/eminsk/nanogemm/blob/main/notebooks/benchmark.ipynb